Heyting-valued interpretations for constructive set theory

Annals of Pure and Applied Logic 137 (1):164-188 (2006)

Abstract
We define and investigate Heyting-valued interpretations for Constructive Zermelo–Frankel set theory . These interpretations provide models for CZF that are analogous to Boolean-valued models for ZF and to Heyting-valued models for IZF. Heyting-valued interpretations are defined here using set-generated frames and formal topologies. As applications of Heyting-valued interpretations, we present a relative consistency result and an independence proof
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/j.apal.2005.05.021
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 38,955
Through your library

References found in this work BETA

Inductively Generated Formal Topologies.Thierry Coquand, Giovanni Sambin, Jan Smith & Silvio Valentini - 2003 - Annals of Pure and Applied Logic 124 (1-3):71-106.
The Strength of Some Martin-Löf Type Theories.Edward Griffor & Michael Rathjen - 1994 - Archive for Mathematical Logic 33 (5):347-385.
Wellfounded Trees in Categories.Ieke Moerdijk & Erik Palmgren - 2000 - Annals of Pure and Applied Logic 104 (1-3):189-218.

View all 11 references / Add more references

Citations of this work BETA

Sublocales in Formal Topology.Steven Vickers - 2007 - Journal of Symbolic Logic 72 (2):463 - 482.

View all 14 citations / Add more citations

Similar books and articles

On Kreisel's Notion of Validity in Post Systems.Dov M. Gabbay - 1976 - Studia Logica 35 (3):285 - 295.
Syntax and Semantics of the Logic.Carsten Butz - 1997 - Notre Dame Journal of Formal Logic 38 (3):374-384.
Henselian Valued Fields: A Constructive Point of View.Hervé Perdry - 2005 - Mathematical Logic Quarterly 51 (4):400-416.
Closed Fragments of Provability Logics of Constructive Theories.Albert Visser - 2008 - Journal of Symbolic Logic 73 (3):1081-1096.
Predicate Logics of Constructive Arithmetical Theories.Albert Visser - 2006 - Journal of Symbolic Logic 71 (4):1311 - 1326.
Generalizing Realizability and Heyting Models for Constructive Set Theory.Albert Ziegler - 2012 - Annals of Pure and Applied Logic 163 (2):175-184.
MV and Heyting Effect Algebras.D. J. Foulis - 2000 - Foundations of Physics 30 (10):1687-1706.

Analytics

Added to PP index
2013-12-31

Total views
15 ( #465,821 of 2,319,409 )

Recent downloads (6 months)
11 ( #85,669 of 2,319,409 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature